Question

The FI Corporation's dividends per share are expected to grow indefinitely by 5% per year. a. If this year’s year-end dividend is $8 and the market capitalization rate is 10% per year, what must the current stock price be according to the dividend discount model? b. If the expected earnings per share are $12, what is the implied value of the ROE on future investment opportunities? (Do not round intermediate calculations. Round your answer to the nearest whole percent.) c. How much is the market paying per share for growth opportunities (that is, for an ROE on future investments that exceeds the market capitalization rate)?

Answer 1

a) Div₁ = $8

Re = 10%

g = 5%

P₀ = Div₁ / (Re - g) = $8 / (10% - 5%) = $8 / 5% = $160

b) we can use the following formula: g = ROE x b

g = growth rate = 5%

b = retention rate = ($12 - $8) / $12 = 0.3333

ROE = g / b = 5% / 33.33% = 15%

c) the present value of growth opportunity (PVGO) = P₀ - EPS / Re = $160 - $12/10% = $160 - $120 = $40

the market is paying $40 for the company's growth opportunity